Analysis of Boundary-Domain Integral Equations based on a new parametrix for the mixed diffusion BVP with variable coefficient in an interior Lipschitz domain

Abstract

A mixed boundary value problem for the partial differential equation of diffusion in an inhomogeneous medium in a Lipschitz domain is reduced to a system of direct segregated parametrix-based Boundary-Domain Integral Equations (BDIEs). We use a parametrix different from the one employed in the papers by Mikhailov (2002, 2006) and Chkadua, Mikhailov, Natroshvili (2009). We prove the equivalence between the original BVP and the corresponding BDIE system. The invertibility and Fredholm properties of the boundary-domain integral operators are also analysed.

arXiv commentarXiv admin note: text overlap with arXiv:1801.03854

References in corpus (2)

• Analysis of Boundary-Domain Integral Equations to the Mixed BVP for a Compressible Stokes System with Variable Viscosity
• Analysis of Segregated Boundary-Domain Integral Equations for BVPs with Non-smooth Coefficient on Lipschitz Domains

Cited by in corpus (2)

• A New Family of Boundary-Domain Integral Equations for the Dirichlet Problem of the Diffusion Equation in Inhomogeneous Media with $H^{-1}(\Omega )$ Source Term on Lipschitz Domains
• Boundary-Domain Integral Equations for the Mixed Problem for the Diffusion Equation in Inhomogeneous Media based on a New Family of Parametrices on Unbounded Domains